If a ladder is not in balance against a smooth vertical wall, then it can be made in balance by :-

Options

A. Decreasing the length of ladder
B. Increasing the length of ladder
C. Increasing the angle of inclination
D. Decreasing the angle of inclination

Answer

To solve the problem of balancing a ladder against a smooth vertical wall, we need to analyze the forces and torques acting on the ladder.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a ladder leaning against a smooth vertical wall. The wall is smooth, which means it does not exert any frictional force on the ladder.
- The ladder has a weight (mg) acting downwards at its center of mass.

2. **Identifying Forces**:
- The weight of the ladder acts downward at its center of mass.
- The wall exerts a normal force perpendicular to its surface at the point where the ladder touches the wall.
- The ground also exerts a normal force and possibly a frictional force at the base of the ladder.

3. **Torque Analysis**:
- To analyze the balance of the ladder, we need to consider the torques acting about the base of the ladder (point on the ground).
- The torque due to the weight of the ladder (mg) can be calculated as:
\[ \text{Torque} = \text{Force} \times \text{Distance} \]
- The distance from the base to the center of mass is \( \frac{L}{2} \cos(\theta) \), where \( L \) is the length of the ladder and \( \theta \) is the angle of inclination with the ground.

4. **Condition for Balance**:
- For the ladder to be in balance, the torque due to the weight of the ladder must be balanced by the torque due to the normal force from the wall.
- If the angle \( \theta \) is increased, the component of the weight acting perpendicular to the ladder decreases (since it involves \( \cos(\theta) \)), thus reducing the torque.

5. **Conclusion**:
- To balance the ladder, we can increase the angle of inclination \( \theta \). This will reduce the torque acting on the ladder, allowing it to remain in a stable position.

### Final Answer:
The ladder can be made in balance by **increasing the angle of inclination**.